Dynamic optimal output feedback control of satellite formation reconfiguration based on an LMI approach

This study presents a dynamic quadratic-optimal (DQO) output feedback controller for satellite formation reconfiguration based on a linear matrix inequality (LMI) approach. A relative motion model involving communication topology of formation flying on a circular reference orbit is established through graph theory. As the design of a static quadratic-optimal (SQO) output feedback controller was determined to be infeasible, emphasis is placed on designing a DQO output feedback controller. Introducing an impulse function enables us to transform the original DQO output feedback control (DQO-OFC) problem into an optimal L₂-norm problem, which can be solved in the standard frame of an LMI approach. It is infeasible to employ a conventional substitution method to treat a nonlinear term with a quadratic form. Thus, an elimination method is adopted in order to address nonlinear terms in the matrix inequalities to obtain a set of equivalent LMIs. Additional control quantities are developed in order to retain the formation configuration in a non-zero state. Simulation results demonstrate validity and functionality of the proposed DQO output feedback controller.